Increasing average period lengths by switching of robust chaos maps in finite precision
School of Natural Sciences and Engineering, National Institute of Advanced Studies, IISc. Campus, Bangalore, 560 012, India
2 Electrical Engineering Department, The Pennsylvania State University, PA, 16801 Pennsylvania, USA
Corresponding author: email@example.com
Grebogi, Ott and Yorke (Phys. Rev. A 38, 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T) of a dynamical system scales as a function of computer precision (ε) and the correlation dimension (d) of the chaotic attractor: T ∼ε-d/2. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.
© EDP Sciences, Springer-Verlag, 2008